[EM] Automatic LIIA Independent of Locking Order

[Gustav Thorzen]

On Fri, 1 May 2026 14:42:58 +0000 (UTC)
Kevin Venzke <stepjak at yahoo.fr> wrote:

>  Hi Gustav,
> 
> Le vendredi 1 mai 2026 à 08:52:30 UTC−5, Gustav Thorzen via Election-Methods <election-methods at lists.electorama.com> a écrit :
> > Ranked Pairs satisfy Local Independence of Irrelevant Alternatives criterion,
> > but I got curious if this property is obtained independently of locking order.
> > 
> > For context, ISDA comes independently of locking order,
> > but ISDA is implied by LIIA + Majority criterion,
> > so I got curious if LIIA is what actually is obtained
> > and ISDA simply followed from it.
> > 
> > I tried to create a proof for a positive result,
> > but quickly discovered I could not figure out how
> > to cover scenarios containing multiple matchups
> > to be locked in at the same time.
> > 
> > Any help would be much appreciated.
> > Gustav
> 
> I've never implemented Ranked Pairs as locking multiple defeats at the same time,
> since there could be cyclic incompatibilities introduced by this. Instead I try to
> traverse all possible orderings (or agree on a random tiebreaker for pairs ahead of
> time). That's not very convenient for proofs, I guess.

Exactly the problem I ran into.
Combinatorial explosion from all edge cases required
to include explicitly limits me to maximum number of candidates,
and my tries to solve this by induction have failed so far.

> > P.S: I have started to suspect I need to fail LIIA
> > for a MMPO locking order to satisfy all of
> > AFB+Mono+LN-Harm+MB-ISDA
> > unless LIIA satisfaction is automatic independently of locking order,
> > and then figured it was interesting enough of a question on its own.
> 
> Maybe you know this, but the MMPO locking order would normally just give you MAM
> itself. The fact that MMPO doesn't normally care about who won or lost each matchup
> makes no difference if you try to lock the stronger one first anyway.

I did not, though I had suspected something similar.
That will save me the effort of Majority-Beat-ifying MAM separatly.
(And hopefully some reuseable edge case management.)
Much appreciated.

> I understand of course that you only want to use the majorities, so you won't end up
> with a copy of MAM.

Yes, also avoiding the AFB and LN-Help/Harm autofailure that
comes from passing regular ISDA.
 
> I am puzzled that you hold out hope for using a locking order to make a method
> satisfying AFB or LNHarm. I feel that from the examples I posted earlier, looking at
> the nature of the issues, one sees that the problem is not the specific rule that
> orders the defeats, but the wide range of effects from adjusting rankings.

I don't really have much "hope" left,
as the counterexamples have eliminated just about
every single idea I had about creating a systems with
AFB+Mono+Mutual Majority+ one of LN-Help/Harm
at their earliest stages (or using slight modifications of them),
Ranked Pairs style or not.
They also eliminated all but two versions of MMPO orderings I had,
which lead me down the path of investigating automatic LIIA
compliance independent of the locking order,
as I have started to suspect satisfying LIIA without it
autocompliance means criteria comptability failure.

At this point I just want the peace of mind from knowing I did
what I could with my last promising looking Ranked Pairs style idea.

Gustav